Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics Chapter 4: Data Handling and Presentation.

 

Class 6 Mathematics – Ganita Prakash

Chapter 4: Data Handling and Presentation

Study Material cum Worksheet

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Chapter Subsections Covered

4.1 Introduction to Data
4.2 Collecting and Organizing Data
4.3 Pictographs
4.4 Bar Graphs
4.5 Line Graphs
4.6 Circle Graphs (Pie Charts – Introductory)
4.7 Central Tendencies – Mean, Median, Mode
4.8 Application of Data Handling in Daily Life

[Insert Image: NCERT Ch.4, Page xx – Example of data table]
[Insert Image: NCERT Ch.4, Page xx – Example of pictograph]
[Insert Image: NCERT Ch.4, Page xx – Example of bar graph]
[Insert Image: NCERT Ch.4, Page xx – Example of line graph]

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Question Bank

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1. Multiple Choice Questions (20)

(already shared above in previous message – included in doc later)

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2. Assertion and Reasoning Questions (20)

Directions: Choose the correct option:
a) A and R are true, R explains A
b) A and R are true, R does not explain A
c) A is true, R is false
d) A is false, R is true

1. A: A pictograph uses symbols to represent data.
   R: Symbols make data easy to understand.
   (Competency: Understanding pictographs)

2. A: A bar graph always has vertical bars.
   R: Bars can be drawn horizontally as well.
   (Competency: Bar graph knowledge)

3. A: Mean is the sum of values divided by number of values.
   R: Mean is also called the average.
   (Competency: Mean calculation)

4. A: Median is the middle value of arranged data.
   R: For even numbers, it is the average of two middle values.
   (Competency: Median concept)

5. A: Mode is always greater than mean.
   R: Mode is the most frequent observation.
   (Competency: Mode understanding)

6. A: Bar graphs can be used to compare categories.
   R: The height/length of bar shows the frequency.
   (Competency: Graph interpretation)

7. A: Line graphs are best to show trends over time.
   R: They connect points representing values over time.
   (Competency: Line graphs)

8. A: In a pie chart, the whole circle represents 100%.
   R: Each sector shows a part of the whole.
   (Competency: Circle graphs)

9. A: The average marks of a class is always equal to the highest marks.
   R: Mean represents the most frequent value.
   (Competency: Misconception check)

10. A: Extreme values affect the mean.
    R: Because mean takes all values into account.
    (Competency: Mean property)

11. A: Data can be qualitative or quantitative.
    R: Favourite colour is qualitative, height is quantitative.
    (Competency: Types of data)

12. A: Frequency means how often a value occurs.
    R: In data 2,2,3,4,2 – frequency of 2 is 3.
    (Competency: Frequency concept)

13. A: A pictograph is always more accurate than a bar graph.
    R: Both are equal in accuracy.
    (Competency: Comparing graphs)

14. A: In a bar graph, width of bar has meaning.
    R: Width can be chosen freely, only height shows data.
    (Competency: Graph construction)

15. A: The sum of percentages in a pie chart is 360%.
    R: A circle has 360°.
    (Competency: Circle graphs misconception check)

16. A: Averages are useful for comparing different groups.
    R: They reduce data to a single value.
    (Competency: Importance of averages)

17. A: Organizing data in a table makes interpretation easier.
    R: It helps to see frequency and patterns.
    (Competency: Data organization)

18. A: Median is not affected by extreme values.
    R: It depends only on middle values.
    (Competency: Properties of median)

19. A: Mode cannot be used for qualitative data.
    R: Mode of favourite fruit survey can be “mango”.
    (Competency: Mode with qualitative data)

20. A: All bar graphs must start from zero.
    R: Scale of graph can start from non-zero for clarity.
    (Competency: Graph scales)

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3. True or False (10)

1. Pictographs always use pictures. (True) (Competency: Pictograph basics)

2. Mean and median are always equal. (False) (Competency: Comparing averages)

3. A line graph can show daily temperature changes. (True) (Competency: Line graph use)

4. Mode is the least occurring observation. (False) (Competency: Mode)

5. Circle graph is also called pie chart. (True) (Competency: Graph types)

6. Data handling is not useful in daily life. (False) (Competency: Real life application)

7. A frequency table shows how often values occur. (True) (Competency: Frequency table)

8. In bar graphs, spaces between bars show categories are separate. (True) (Competency: Bar graph reading)

9. Mean is not affected by extreme values. (False) (Competency: Mean property)

10. Tables, charts and graphs are ways of data presentation. (True) (Competency: Data presentation)

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4. Short Answer I – 2 Marks (15)

1. Define data with an example. (Competency: Basic definition)

2. Represent marks of 5 students: 15, 18, 20, 22, 25 in a table. (Competency: Data organization)

3. What does each bar in a bar graph represent? (Competency: Graph reading)

4. A pictograph uses 🍎 = 5 apples. Draw for 15 apples. (Competency: Pictograph drawing)

5. Define frequency. (Competency: Data terms)

6. Mean of 4, 6, 8. (Competency: Mean)

7. Median of 2, 5, 7. (Competency: Median)

8. Mode of 3, 4, 4, 5, 6. (Competency: Mode)

9. Which type of data: (i) Colour of eyes (ii) Height of students. (Competency: Data classification)

10. What is a pie chart? (Competency: Circle graph definition)

11. Draw a bar graph for 3 fruits: Apple=10, Mango=15, Banana=20. (Competency: Bar graph)

12. Give 2 advantages of data handling. (Competency: Importance of data)

13. A student has 5 absences in 30 days. Represent in pictograph (1 symbol=5 days). (Competency: Pictograph)

14. What is range of data 12,15,20,22? (Competency: Range)

15. Write difference between discrete and continuous data. (Competency: Data types)

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5. Short Answer II – 3 Marks (10)

1. Mean of 10, 20, 30, 40, 50. (Competency: Mean)

2. Find median of 5, 7, 9, 11, 15, 17. (Competency: Median)

3. Mode of 2, 3, 3, 4, 5, 5, 5, 6. (Competency: Mode)

4. Draw bar graph: Red=5, Blue=7, Green=3. (Competency: Bar graph construction)

5. In a pictograph, 🍎 = 2 books. Show 8 books. (Competency: Pictograph)

6. Marks of 5 students: 10, 12, 15, 20, 25. Find range. (Competency: Range)

7. Explain with example how mean can be misleading. (Competency: Limitations of mean)

8. A survey of pets: Dog=6, Cat=4, Fish=2. Represent as pictograph. (Competency: Pictograph drawing)

9. Find total marks if mean = 15 and number of students = 12. (Competency: Mean application)

10. Construct frequency table: Data = 2,3,2,4,3,3,5. (Competency: Data tabulation)

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6. Long Answer Questions – 5 Marks (10)

1. Marks of 10 students: 5,6,6,7,7,7,8,8,9,10. Find mean, median, mode. (Competency: Central tendency)

2. Daily temperature (°C): 30,32,31,33,32,30,29. Draw line graph. (Competency: Line graph)

3. A survey of favourite sports: Cricket=20, Football=15, Hockey=10, Tennis=5. Draw bar graph. (Competency: Bar graph)

4. A pie chart represents monthly expenses: Rent 120°, Food 90°, Travel 60°, Others 90°. Explain. (Competency: Pie chart)

5. 10 students scored marks: 15,18,20,22,25,30,32,35,36,40. Find mean. (Competency: Mean)

6. Attendance in 5 days: 35,36,34,37,38. Represent in table and bar graph. (Competency: Data tabulation and representation)

7. Discuss 3 uses of data handling in daily life. (Competency: Application)

8. Find range and mean: 2,4,6,8,10. (Competency: Range & mean)

9. A class test: 5 students scored 10,15,15,20,25. Find median. (Competency: Median)

10. Why is mode useful in daily life? Give examples. (Competency: Mode application)

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7. Case-Based Questions (5 Sets, 4 MCQs each)

Case Study 1 (Pictograph – Fruits)

A pictograph shows fruit sales. 🍎=5 fruits.
Apples=20, Mangoes=25, Oranges=15, Bananas=10.
[Insert Image: NCERT pictograph example]

Q1. How many apples sold?
a) 20 b) 25 c) 15 d) 10

Q2. Which fruit sold most?
a) Apple b) Mango c) Orange d) Banana

Q3. Total fruits sold?
a) 70 b) 60 c) 50 d) 40

Q4. Which fruit sold least?
a) Banana b) Orange c) Apple d) Mango

(Competency: CBQ – Pictograph interpretation)

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Case Study 2 (Bar Graph – Sports)

Bar graph shows favourite sports of 40 students: Cricket=15, Football=10, Hockey=8, Tennis=7.
[Insert Image: NCERT bar graph example]

Q1. Which sport most popular?
a) Cricket b) Football c) Hockey d) Tennis

Q2. How many students like Tennis?
a) 5 b) 7 c) 10 d) 15

Q3. Total students surveyed?
a) 20 b) 30 c) 40 d) 50

Q4. Difference between Cricket and Tennis lovers?
a) 5 b) 7 c) 8 d) 10

(Competency: CBQ – Bar graph interpretation)

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Case Study 3 (Line Graph – Temperature)

Line graph shows temperatures for 5 days: Mon=30, Tue=32, Wed=33, Thu=31, Fri=29.
[Insert Image: NCERT line graph example]

Q1. Highest temperature recorded?
a) 29 b) 30 c) 32 d) 33

Q2. Lowest temperature recorded?
a) 29 b) 30 c) 31 d) 32

Q3. On which day was 32°C recorded?
a) Monday b) Tuesday c) Wednesday d) Thursday

Q4. Difference between highest and lowest?
a) 2°C b) 3°C c) 4°C d) 5°C

(Competency: CBQ – Line graph interpretation)

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Case Study 4 (Pie Chart – Expenditure)

A family’s monthly budget: Rent 120°, Food 90°, Travel 60°, Others 90°.
[Insert Image: NCERT pie chart example]

Q1. Which category largest share?
a) Rent b) Food c) Travel d) Others

Q2. Which two categories equal?
a) Rent & Food b) Travel & Others c) Food & Others d) Rent & Travel

Q3. Angle for Rent?
a) 60° b) 90° c) 120° d) 180°

Q4. Total degrees of pie chart?
a) 90° b) 180° c) 270° d) 360°

(Competency: CBQ – Pie chart reading)

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Case Study 5 (Frequency Table – Attendance)

Attendance of 6 days: 35,34,36,35,37,36.
Table prepared for frequencies.
[Insert Image: NCERT frequency table example]

Q1. Most frequent attendance?
a) 34 b) 35 c) 36 d) 37

Q2. Range of data?
a) 1 b) 2 c) 3 d) 4

Q3. Mean attendance?
a) 35 b) 35.5 c) 36 d) 37

Q4. Median attendance?
a) 35 b) 35.5 c) 36 d) 37

(Competency: CBQ – Frequency table interpretation)